On Modeling,Analysis And Application In Chaotic Circuit Of Nano SBT Memristor

In 2008,Hewlett-Packard Laboratory realized the first workable memristor prototype in the world,confirming the theory of memristor proposed by L.O.Chua decades ago.It is predicted that there should exist a fourth basic two-terminal element in the circuit,besides resistor,capacitor and inductor,which is called memristor,a kind of resistor with memory.The appearance of HP memristor has attracted worldwide attention.As a new basic circuit element,memritor provides a new space for development to circuit theoritical research and design.It is evaluated as an electronic device that will have a significant impact on the development of electronic science and will bring fundamental changes in circuit theory.Besides,due to their nanoscale structure,non-volatility,synaptic function,low power consumption and compatibility with traditional integrated circuits,memristors are promising in high integration memory,large scale integrated circuit,artificial neural network,reconfigurable logic and programmable logic,pattern recognition,signal processing,and nonlinear circuit system.It has become a hotspot in international research field in recent years.In this dissertation,based on nano SBT(Sr0.95Ba0.05TiO3)memristor prepared in the previous work of the laboratory,its physical and mathematical models are established,and a series of memrisive chaotic circuits and systems are constructed,and their complex dynamic behaviors are analyzed.The main research contents and innovations are as follows:(1)By analyzing the physical mechanism of nano SBT memristor,the voltage-controlled physical model is established.Its corresponding flux-controlled mathematical model is proposed.Based on the experimental data,the parameters of the mathematical model are determined by numerical analysis method.By comparing the u-i characteristic curve of the memristor simulated by the mathematical model with the actually measured curves,it is confirmed that the model is accurate and reliable,and can be used to describe the dynamic characteristics of nano SBT memristor,so that it can be used as a known circuit element in the design of nonlinear circuits.(2)On the basis of this mathematical model,the basic characteristics of nano SBT memristors are analyzed.The influences of amplitude,initial phase of sinusoidal periodic voltage signal and initial state value of memristor on its u-i characteristic curve are studied.In addition,with the increase of frequency of periodic voltage signal,the variation of lobe area around the characteristic curve is also investigated.The analysis results show that the nano SBT memristor has all the basic characteristics of memristor.(3)Self-excited oscillatory circuit,forced oscillatory circuit and forced chaotic oscillatory circuit are built on nano SBT memristor,in which stable periodic oscillations,quasi-periodic oscillations and chaotic oscillations are generated respectively.The circuit construction shows that when the linear inductor is in parallel with the memristor,the order of the circuit system is 1 less than the number of energy storage elements,and the equilibrium point of the self-excited oscillatory circuit system is no longer typical line equilibrium.In addition,external driving voltage source will increase the order and dynamical complexity of the circuit system.The numerical simulation results show that the state,amplitude and frequency of oscillations in the three circuit systems are affected by the parameters of the circuit elements,but when the linear inductor is in parallel with the memristor,the oscillatory behaviors in the circuit systems will not be affected by the initial state value of the SBT memristor.(4)A chaotic circuit based on nano SBT memristor is constructed.Nano SBT memristor and a linear negative resistor are connected in parallel to substitute the Chua's diode in the Chua's circuit,and chaotic signals are generated.The chaotic circuit can be modeled as a fourth-order nonlinear system in voltage-current space and a third-order nonlinear system in flux-charge space,respectively.The numerical simulation results show that different circuit element parameters and initial state values of nano SBT memristor lead to a variety of complex dynamic behaviors in the circuit system,including stable sinks,periods,chaos and other complex transient dynamic behaviors.The results are consistent with the theoretical stability analysis.